Chapter 8.9, Problem 11E

To determine

What are some possible combinations of matinees and evening shows that you can see?

Answer to Problem 11E

You can see 0 matinees and 5 evening shows, or 3 matinees and 3 evening shows, or 8 matinees and 0 evening shows.

Explanation of Solution

Given:

You have a gift certificate for $40 to use at a movie theater. Matinees cost $5 and evening shows cost $8.

Calculation:

Let x represent number of matinees shows and y represent number of evening shows.

We have been given that matinees cost $5, so cost of x matinees would be $5x$ .

We are also told that evening shows cost $8, so cost of y evening shows would be $8y$ .

Since you have a gift certificate for $40 to use at a movie theater, so total cost of x matinees and y evening shows should be less than or equal to $40. We can represent this information in an inequality as:

  $5x+8y\le 40$

Upon graphing our inequality, we will get our required graph as shown below:

  

Upon looking at our given inequality, we can see that points $(0,5),(3,3)\text{ and (8,0)}$ satisfy our inequality. Therefore, you can see 0 matinees and 5 evening shows, or 3 matinees and 3 evening shows, or 8 matinees and 0 evening shows.